Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Resultados 6-10 de 18
Página 54
... Substituting in equa . ( 12 ) , for cos a its equiva- lent 2 cos2 A - 1 , we have COS A = · [ a + b + c ] · [ } ( a + b + c ) — a ] bc .... ( 13. ) If , in equa . ( 11 ) we substitute 1 2 sin2 A for ' Cos A , we shall have 2 sin1A = 1 + ...
... Substituting in equa . ( 12 ) , for cos a its equiva- lent 2 cos2 A - 1 , we have COS A = · [ a + b + c ] · [ } ( a + b + c ) — a ] bc .... ( 13. ) If , in equa . ( 11 ) we substitute 1 2 sin2 A for ' Cos A , we shall have 2 sin1A = 1 + ...
Página 85
... substituting for cos b in the third of the equations marked ( 2 ) its value in the second ; substi- tuting also for cos2 a its value 1 - sin2 a ( chap . i . 19 ) , and striking out the common factor sin a , we shall have cos c sin a sin ...
... substituting for cos b in the third of the equations marked ( 2 ) its value in the second ; substi- tuting also for cos2 a its value 1 - sin2 a ( chap . i . 19 ) , and striking out the common factor sin a , we shall have cos c sin a sin ...
Página 129
... equa . 6 ) , COS PD COS PE COS DE sin AP COS DE ; and , therefore , sec PD = COS PD 1 . sin APCOS DE Substituting this in the last value of st2 , we have St2 sec2 AP + tan2 PD sec2 AP + tan2 G 5 Stereographic Projection . 129.
... equa . 6 ) , COS PD COS PE COS DE sin AP COS DE ; and , therefore , sec PD = COS PD 1 . sin APCOS DE Substituting this in the last value of st2 , we have St2 sec2 AP + tan2 PD sec2 AP + tan2 G 5 Stereographic Projection . 129.
Página 133
... substituting for cos CM , sin cм , their values in tan CM , & c . deduced by means of equa . R , chap . iv . 47. The projections here treated serving for the usual purposes of astronomy , we need not enter upon the explication of the ...
... substituting for cos CM , sin cм , their values in tan CM , & c . deduced by means of equa . R , chap . iv . 47. The projections here treated serving for the usual purposes of astronomy , we need not enter upon the explication of the ...
Página 144
... Substituting H for мb in the former of these , and making the terms homogeneous , we have sin 90 ° tan H = cos L tan P. This equation is similar to the equation of the hour angles in the horizontal dial ; and the construction will ...
... Substituting H for мb in the former of these , and making the terms homogeneous , we have sin 90 ° tan H = cos L tan P. This equation is similar to the equation of the hour angles in the horizontal dial ; and the construction will ...
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith